> I am late to this party and do not have time to read the conversation but I have learned not to trust Keith Devlin's interest in developing genuine mathematics competence but, rather, to satisfy the much more popular interest of mathematics education writers and other progressives. Although he is at Stanford, he does not consult with their top-notch department of mathematics; most of them don't know that he is even there in spite of his well-respected expertise.

What would he consult with them about? If you read his description at Stanford -

"His current research is focused on the use of different media to teach and communicate mathematics to diverse audiences.?

It isn?t that unordinary that he wouldn?t be hanging out with the math-dept every chance he gets. Their mission is mathematics.

I think all of us know by now what ?teach and communicate mathematics to diverse audiences? means. 10 years ago I didn?t know. And 20 years ago I don?t think the phrase even existed. And when you read it, it doesn?t make a lot of sense. Looking up descriptions and definitions of what it means doesn?t help either because the definitions become circular. The only way to actually know what it means is to see examples of what it means. And that takes a bit of effort, more than the casual observer often has time for.

Taken literally, it would seem to mean that when you teach mathematics to a class with a mixture of ethnic groups that you must teach it differently. But I could find no evidence at all that mathematics achievement is based on ethnicity. What I mean is, that when I compared students across the world and across every demographic factor possible, you could not distinguish between them based on how well they did on tests. If you looked at a group of students, all scoring 80, on the same test, but scattered all over the globe, you could not tell who was who by examining the items they got right or wrong.

So it can?t mean that you must teach mathematics one way to one ethnic group and a different way to another, or a third way when the groups are combined.

But then what does it mean?

Another option is that it means how to teach mathematics to a class diverse in ability. But then what does that mean? 3rd graders with 6th graders? That doesn?t make a lot sense either.

As I said, you have to go out and observe examples to understand what teaching mathematics to diverse audiences means.

When you do that, then you realize that the confusion you had all along wasn?t due to the word ?diverse?. It was due to the word ?teaching?.

Essentially, it means how to present advanced mathematical topics to lay persons.

Now it makes a lot of sense. In fact, now the course makes a lot of sense. Indeed, now many courses make a lot of sense.

And Dr. Devlin certainly has a lot of talent in this regard, more than I for sure.